"The House has made its position known very clearly," Boehner said in his statement, flanked by other members of the House GOP leadership team.

"We believe we should fund government, and we think there ought to basic fairness for all Americans under Obamacare. The Senate has continued to reject our offers, but under the Constitution, there's a way to resolve this problem — and that is to go to conference and talk through your differences. And I would hope that the Senate would accept our offer to go to conference and discuss this so that we can resolve this for the American people."